Question: Which of the following numbers is a factor of 84? ${5,7,8,10,11}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $84$ by each of our answer choices. $84 \div 5 = 16\text{ R }4$ $84 \div 7 = 12$ $84 \div 8 = 10\text{ R }4$ $84 \div 10 = 8\text{ R }4$ $84 \div 11 = 7\text{ R }7$ The only answer choice that divides into $84$ with no remainder is $7$ $ 12$ $7$ $84$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $7$ are contained within the prime factors of $84$ $84 = 2\times2\times3\times7 7 = 7$ Therefore the only factor of $84$ out of our choices is $7$. We can say that $84$ is divisible by $7$.